Tried a ring and it doesn't work. It can't pass the stopper or even the bar when released.

Ended up with a small SS washer which I've glued on this big hole just to try with. So the bungee stops at the washer.
And man, what a difference with this swivel. I've been out today for 3hrs, made 40km it total.
Lines perfectly straight after a lot of looping. I can see that the middle line is twisted. That is because it cannot spin in this setup. Will try to do something and post the results.